Moe (pronounced MO-EH) is a common female given name in Japanese. Famous Moes include Japanese model Moe Oshikiri, Japanese actress Moe Yamaguchi, Japanese model Moe Kirimura, Japanese Olympic curler Moe Meguro, Japanese pornstar Moe Kimishima, and Japanese actress Moe Arai.
The basic meaning of the name Moe is "sprout" or "bud" and the most obvious way to write this in Japanese is by using the Chinese character for "sprout" along with the Japanese phonetic character for the sound "e" (萌え).
If you can imagine naming a little girl "Sprout" in English, you can see why this name tends to have a very cutesy feel in Japanese. It's not exactly a name you'd give your daughter if you entertain hopes she'll grow up to be a doctor or supreme court justice.
Perhaps this is why, in recent times, the name Moe is often written entirely in the Japanese phonetic syllabary hiragana, without using any Chinese-derived kanji characters, as simply もえ. However, according to ENAMDICT there are 61 known ways to write the name Moe in Japanese.
The most common alternative writings substitute another character with a pleasing meaning for the phonetic "e", such as "glory" (萌英 = "glorious sprout"), "branch" (萌枝 = "budding branch"), "picture" (萌絵 = "picture of buds"), "inlet" (萌江 = "verdant inlet"), or "blessing" (萌恵 = "sprouted blessing").
Nevertheless, there do exist a few more quirky or interesting variants, including 雲燕 ("cloud swallow"), 最燃 ("the most burnt"), 望愛 ("moon love"), 藻恵 ("seaweed blessing"), 桃愛 ("peachtree love") and my personal favorite, 百笑 ("one hundred smiles").
I think I definitely would have liked to have had the option of naming my daughter "one hundred smiles."
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